A363511 Number of partitions of [n] having exactly one parity change within their blocks.
0, 0, 1, 2, 6, 18, 61, 210, 778, 3008, 12219, 52268, 231726, 1083012, 5202199, 26307710, 135972580, 738339310, 4081523615, 23649300862, 139096468520, 855529383396, 5329630673249, 34643027568520, 227682351175868, 1558106351450416, 10766192988109009
Offset: 0
Keywords
Examples
a(4) = 6: 124|3, 12|3|4, 134|2, 1|23|4, 14|2|3, 1|2|34.
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..500
- Wikipedia, Partition of a set
Programs
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Maple
b:= proc(n, x, y) option remember; convert(series( `if`(n=0, 1, `if`(y=0, 0, expand(b(n-1, y-1, x+1)*y*z)) +b(n-1, y, x)*x + b(n-1, y, x+1)), z, 2), polynom) end: a:= n-> coeff(b(n, 0$2), z, 1): seq(a(n), n=0..27);